Temporal patterns of alpha 1-receptor stimulation regulate amplitude and frequency of calcium transients

A Spatial Model of Hepatic Calcium Signaling and Glucose Metabolism Under Autonomic Control Reveals Functional Consequences of Varying Liver Innervation Patterns Across Species

Rapid breakdown of hepatic glycogen stores into glucose plays an important role during intense physical exercise to maintain systemic euglycemia. Hepatic glycogenolysis is governed by several different liver-intrinsic and systemic factors such as hepatic zonation, circulating catecholamines, hepatocellular calcium signaling, hepatic neuroanatomy, and the central nervous system (CNS). Of the factors regulating hepatic glycogenolysis, the extent of lobular innervation varies significantly between humans and rodents. While rodents display very few autonomic nerve terminals in the liver, nearly every hepatic layer in the human liver receives neural input. In the present study, we developed a multi-scale, multi-organ model of hepatic metabolism incorporating liver zonation, lobular scale calcium signaling, hepatic innervation, and direct and peripheral organ-mediated communication between the liver and the CNS. We evaluated the effect of each of these governing factors on the total hepatic glucose output and zonal glycogenolytic patterns within liver lobules during simulated physical exercise. Our simulations revealed that direct neuronal stimulation of the liver and an increase in circulating catecholamines increases hepatic glucose output mediated by mobilization of intracellular calcium stores and lobular scale calcium waves. Comparing simulated glycogenolysis between human-like and rodent-like hepatic innervation patterns (extensive vs. minimal) suggested that propagation of calcium transients across liver lobules acts as a compensatory mechanism to improve hepatic glucose output in sparsely innervated livers. Interestingly, our simulations suggested that catecholamine-driven glycogenolysis is reduced under portal hypertension. However, increased innervation coupled with strong intercellular communication can improve the total hepatic glucose output under portal hypertension. In summary, our modeling and simulation study reveals a complex interplay of intercellular and multi-organ interactions that can lead to differing calcium dynamics and spatial distributions of glycogenolysis at the lobular scale in the liver.

Pyomelanin produced by Streptomyces sp. ZL-24 and its protective effects against SH-SY5Y cells injury induced by hydrogen peroxide

A soluble melanin pigment produced by Streptomyces sp. ZL-24 was purified and named StrSM. The elemental analysis of StrSM showed it consists of carbon, hydrogen, and oxygen. The spectrum analysis, including ultraviolet-visible absorption spectrum, Fourier-transform infrared spectrum, and pyrolysis-gas chromatography-mass spectrometry, indicated that StrSM might be pyomelanin. High performance liquid chromatography and liquid chromatography-mass spectra analysis of intermediate metabolite showed the presence of homogentisic acid (HGA). Moreover, the enzyme 4-hydroxyphenylpyruvate dioxygenase, involved in HGA biosynthesis, showed high activity during melanin production. Subsequently, a tyrosinase gene (melC2) and hydroxyphenylpyruvate dioxygenase gene double mutant demonstrated StrSM is pyomelanin. In vitro bioactivity assay showed that StrSM had excellent protective capability against SH-SY5Y cell oxidative injury. To our knowledge, the results firstly provide comprehensive data on Streptomyces pyomelanin identification and a promising candidate compound to treat oxidative injury of neurocytes.

Linear Channel Modeling and Error Analysis for Intra/Inter-Cellular Ca2+ Molecular Communication

The use of intra/inter-cellular calcium ion (Ca²⁺) signaling for molecular communication (MC) is investigated in this paper. In particular, the elevation of the intracellular Ca²⁺ concentration upon the external excitation, i.e., Ca²⁺ wave generation, and the intercellular propagation of Ca²⁺ wave over consecutive cells are studied for information transmission. The main objective of this paper is to develop a linear channel model for intra/inter-cellular Ca²⁺ MC. In this context, the end-to-end Ca²⁺ MC system is studied under three blocks: the wave generation, the gap junctional (intercellular) propagation, and the intracellular propagation. The wave generation block captures the intracellular Ca²⁺ signaling pathway including the release of Ca²⁺ from the organelles and the buffers inside a cell, and the intake from the extracellular space. The gap junctional (intercellular) propagation block captures the Ca²⁺ transition through the gap junctions between the touching cells. The intracellular propagation block defines the effect of the cytoplasmic diffusion. Using the developed blocks for the different biophysical phenomena, the end-to-end channel gain and delay formulas are derived. Furthermore, the bit error probability is studied to reveal the impact of the detection threshold. This work provides the basis for the modeling, analysis and the design of Ca²⁺ MC systems.

Cellular Interrogation: Exploiting Cell-to-Cell Variability to Discriminate Regulatory Mechanisms in Oscillatory Signalling

The molecular complexity within a cell may be seen as an evolutionary response to the external complexity of the cell’s environment. This suggests that the external environment may be harnessed to interrogate the cell’s internal molecular architecture. Cells, however, are not only nonlinear and non-stationary, but also exhibit heterogeneous responses within a clonal, isogenic population. In effect, each cell undertakes its own experiment. Here, we develop a method of cellular interrogation using programmable microfluidic devices which exploits the additional information present in cell-to-cell variation, without requiring model parameters to be fitted to data. We focussed on Ca²⁺ signalling in response to hormone stimulation, which exhibits oscillatory spiking in many cell types and chose eight models of Ca²⁺ signalling networks which exhibit similar behaviour in simulation. We developed a nonlinear frequency analysis for non-stationary responses, which could classify models into groups under parameter variation, but found that this question alone was unable to distinguish critical feedback loops. We further developed a nonlinear amplitude analysis and found that the combination of both questions ruled out six of the models as inconsistent with the experimentally-observed dynamics and heterogeneity. The two models that survived the double interrogation were mathematically different but schematically identical and yielded the same unexpected predictions that we confirmed experimentally. Further analysis showed that subtle mathematical details can markedly influence non-stationary responses under parameter variation, emphasising the difficulty of finding a “correct” model. By developing questions for the pathway being studied, and designing more versatile microfluidics, cellular interrogation holds promise as a systematic strategy that can complement direct intervention by genetics or pharmacology.

We have developed a cellular interrogation methodology that combines programmable microfluidics, fluorescence microscopy and mathematical analysis and have used it to discriminate between models of repetitive Ca²⁺ spiking in HeLa cells. Our approach exploits the natural variability in response of individual cells in a clonal population and the non-steady state behavior of the response in each cell, thereby providing more powerful discrimination. Interrogation consists of steps or pulses of histamine of fixed concentration and width but varying frequency. Eight mathematical models of repetitive Ca²⁺ spiking were chosen from the literature and methods of nonlinear frequency and nonlinear amplitude analysis were developed which ruled out all but two of the models, without having to fit the models to the data. Further analysis of the remaining models yielded predictions that were experimentally confirmed. Cellular interrogation offers a general approach to ruling out competing hypotheses about molecular mechanisms, which is complementary to traditional methods of genetics and biochemistry.

Membrane potential and Ca2+ concentration dependence on pressure and vasoactive agents in arterial smooth muscle: A model

A mathematical model incorporating junctional and stretch-activated microdomains and 37 protein components describes the myogenic response in arterial smooth muscle cells.

Arterial smooth muscle (SM) cells respond autonomously to changes in intravascular pressure, adjusting tension to maintain vessel diameter. The values of membrane potential (V_m) and sarcoplasmic Ca²⁺ concentration (Ca_in) within minutes of a change in pressure are the results of two opposing pathways, both of which use Ca²⁺ as a signal. This works because the two Ca²⁺-signaling pathways are confined to distinct microdomains in which the Ca²⁺ concentrations needed to activate key channels are transiently higher than Ca_in. A mathematical model of an isolated arterial SM cell is presented that incorporates the two types of microdomains. The first type consists of junctions between cisternae of the peripheral sarcoplasmic reticulum (SR), containing ryanodine receptors (RyRs), and the sarcolemma, containing voltage- and Ca²⁺-activated K⁺ (BK) channels. These junctional microdomains promote hyperpolarization, reduced Ca_in, and relaxation. The second type is postulated to form around stretch-activated nonspecific cation channels and neighboring Ca²⁺-activated Cl⁻ channels, and promotes the opposite (depolarization, increased Ca_in, and contraction). The model includes three additional compartments: the sarcoplasm, the central SR lumen, and the peripheral SR lumen. It incorporates 37 protein components. In addition to pressure, the model accommodates inputs of α- and β-adrenergic agonists, ATP, 11,12-epoxyeicosatrienoic acid, and nitric oxide (NO). The parameters of the equations were adjusted to obtain a close fit to reported V_m and Ca_in as functions of pressure, which have been determined in cerebral arteries. The simulations were insensitive to ±10% changes in most of the parameters. The model also simulated the effects of inhibiting RyR, BK, or voltage-activated Ca²⁺ channels on V_m and Ca_in. Deletion of BK β1 subunits is known to increase arterial–SM tension. In the model, deletion of β1 raised Ca_in at all pressures, and these increases were reversed by NO.

A comprehensive analysis of strength-based optimum signal detection in concentration-encoded molecular communication with spike transmission

In this paper, a comprehensive analysis of strength-based optimum signal detection model has been presented for concentration-encoded molecular communication (CEMC) with spike (i.e., impulsive) transmission based on amplitude-shift keying (ASK) and on-off keying (OOK) modulations. Strength-based optimum signal detection problem in diffusion-based CEMC system has been investigated in detail in the presence of both diffusion noise and intersymbol interference (ISI). The receiver for optimum signal detection has been developed theoretically and explained with both analytical and simulation results of binary signal detection. Results show that the receiver thus developed can detect CEMC symbols effectively; however, the performance is influenced by three main factors, namely, communication range, transmission data rate, and receiver memory. For both ASK and OOK receivers, exact and approximate detection performances have been derived analytically depending on the probabilistic nature of molecular availability and the relationship between mean and variance of signal strengths. Correspondingly, bit error rate (BER) performance of the optimum receiver in a single CEMC link is further evaluated under various scenarios through extensive simulation experiments.

Spatial Quantification of Cytosolic Ca²⁺ Accumulation in Nonexcitable Cells: An Analytical Study

Calcium ions act as messengers in a broad range of processes such as learning, apoptosis, and muscular movement. The transient profile and the temporal accumulation of calcium signals have been suggested as the two main characteristics in which calcium cues encode messages to be forwarded to downstream pathways. We address the analytical quantification of calcium temporal-accumulation in a long, thin section of a nonexcitable cell by solving a boundary value problem. In these expressions we note that the cytosolic Ca(2+) accumulation is independent of every intracellular calcium flux and depends on the Ca(2+) exchange across the membrane, cytosolic calcium diffusion, geometry of the cell, extracellular calcium perturbation, and initial concentrations. In particular, we analyse the time-integrated response of cytosolic calcium due to i) a localised initial concentration of cytosolic calcium and ii) transient extracellular perturbation of calcium. In these scenarios, we conclude that i) the range of calcium progression is confined to the vicinity of the initial concentration, thereby creating calcium microdomains; and ii) we observe a low-pass filtering effect in the response driven by extracellular Ca(2+) perturbations. Additionally, we note that our methodology can be used to analyse a broader range of stimuli and scenarios.

Microfluidic interrogation and mathematical modeling of multi-regime calcium signaling dynamics

Through microfluidic interrogation we analyzed real-time calcium responses of HEK293 cells stimulated with short pulses of the M3 muscarinic receptor ligand carbachol in two different concentration regimes. Lower ligand concentrations elicit oscillatory calcium signals while higher concentrations trigger a rapid rise that eventually settles down at a steady-state slightly above pre-stimulus levels, referred to as an acute signal. Cells were periodically pulsed with carbachol at these two concentration regimes using a custom-made microfluidic platform, and the resulting calcium signals were measured with a single fluorescent readout. Pulsed stimulations at these two concentration regimes resulted in multiple types of response patterns that each delivered complementary information about the M3 muscarinic receptor signaling pathway. These multiple types of calcium response patterns enabled development of a comprehensive mathematical model of multi-regime calcium signaling. The resulting model suggests that dephosphorylation of deactivated receptors is rate limiting for recovery of calcium signals in the acute regime (high ligand concentration), while calcium replenishment and IP3 production determine signal recovery in the oscillatory regime (low ligand concentration). This study not only provides mechanistic insight into multi-regime signaling of the M3 muscarinic receptor pathway, but also provides a general strategy for analyzing multi-regime pathways using only one fluorescent readout.

Hi-Fi transmission of periodic signals amid cell-to-cell variability

Since information in intracellular calcium signaling is often frequency encoded, it is physiologically critical and experimentally useful to have reliable, convenient, and non-invasive methods to entrain it. Because of cell-to-cell variability, synchronization of intracellular signaling across a population of genetically identical cells can still be difficult to achieve. For intrinsically oscillatory signaling pathways, such as calcium, upon continuous stimulation, cell-to-cell variability is manifested as differences in intracellular response frequencies. Even with entrainment using periodic stimulation, cell-to-cell variability is manifested as differences in the fidelity with which extracellular inputs are converted into intracellular signals. Here we present a combined theoretical and experimental analysis that shows how to appropriately balance stimulation strength, duration, and rest intervals to achieve entrainment with high fidelity stimulation-to-response ratios for G-protein-coupled receptor-triggered intracellular calcium oscillations. We further demonstrate that stimulation parameters that give high fidelity entrainment are significantly altered upon changes in intracellular enzyme levels and cell surface receptor levels. Theoretical analysis suggests that, at key threshold values, even small changes in these protein concentrations or activities can result in precipitous changes in entrainment fidelity, with implications for pathophysiology.

Understanding the temporal codes of intra-cellular signals

The health of organisms and cells depends on appropriate responses to diverse internal and external cues, stimuli, or challenges, such as changes in hormone or cytokine levels, or exposure to a pathogen. Cellular responses must be tailored to the identity and intensity of the stimulus and therefore intra-cellular signals must carry information about both. However, signaling mediators often form intricate networks that react to multiple stimuli yet manage to produce stimulus-specific responses. The multi-functionality ('functional pleiotropism') of signaling nodes suggests that biological networks have evolved ways of passing physiologically relevant stimulus information through shared channels. Increasing evidence supports the notion that this is achieved in part through temporal regulation of signaling mediators' activities. The present challenge is to identify the features of temporal activity profile that represent information about a given stimulus and understand how cells read the temporal codes to control their responses.

ATP-mediated cell-cell signaling in the organ of Corti: the role of connexin channels

Connexin 26 (Cx26) and connexin 30 (Cx30) form hemichannels that release ATP from the endolymphatic surface of cochlear supporting and epithelial cells and also form gap junction (GJ) channels that allow the concomitant intercellular diffusion of Ca(2+) mobilizing second messengers. Released ATP in turn activates G-protein coupled P2Y(2) and P2Y(4) receptors, PLC-dependent generation of IP(3), release of Ca(2+) from intracellular stores, instigating the regenerative propagation of intercellular Ca(2+) signals (ICS). The range of ICS propagation is sensitive to the concentration of extracellular divalent cations and activity of ectonucleotidases. Here, the expression patterns of Cx26 and Cx30 were characterized in postnatal cochlear tissues obtained from mice aged between P5 and P6. The expression gradient along the longitudinal axis of the cochlea, decreasing from the basal to the apical cochlear turn (CT), was more pronounced in outer sulcus (OS) cells than in inner sulcus (IS) cells. GJ-mediated dye coupling was maximal in OS cells of the basal CT, inhibited by the nonselective connexin channel blocker carbenoxolone (CBX) and absent in hair cells. Photostimulating OS cells with caged inositol (3,4,5) tri-phosphate (IP(3)) resulted in transfer of ICS in the lateral direction, from OS cells to IS cells across the hair cell region (HCR) of medial and basal CTs. ICS transfer in the opposite (medial) direction, from IS cells photostimulated with caged IP(3) to OS cells, occurred mostly in the basal CT. In addition, OS cells displayed impressive rhythmic activity with oscillations of cytosolic free Ca(2+) concentration ([Ca(2+)](i)) coordinated by the propagation of Ca(2+) wavefronts sweeping repeatedly through the same tissue area along the coiling axis of the cochlea. Oscillations evoked by uncaging IP(3) or by applying ATP differed greatly, by as much as one order of magnitude, in frequency and waveform rise time. ICS evoked by direct application of ATP propagated along convoluted cellular paths in the OS, which often branched and changed dynamically over time. Potential implications of these findings are discussed in the context of developmental regulation and cochlear pathophysiology.

ELECTRONIC SUPPLEMENTARY MATERIAL

The online version of this article (doi:10.1007/s11302-010-9192-9) contains supplementary material, which is available to authorized users.

Guattegaumerine protects primary cultured cortical neurons against oxidative stress injury induced by hydrogen peroxide concomitant with serum deprivation

Guattegaumerine is a natural product with characteristics of being lipophilic and reaching high concentration in the brain, but its function in the central nervous system has not yet been observed. This study was designed to evaluate the neuroprotective effects of guattegaumerine on rat primary cultured cortical neurons. Following a 24-h exposure of the cells to combined serum-starvation and hydrogen peroxide, a significant augment in neuron damage as determined by 3-(4,5-dimethylthiazol-2-yl)-2, 5-diphenyl-tetrazolium bromide (MTT) assay and lactate dehydrogenase (LDH) release were observed. Preincubation of guattegaumerine dramatically improved the cell viability and inhibited LDH release. Preincubation of guattegaumerine also dramatically inhibited malondialhehyde (MDA) production and elevated the decreased total antioxidative capacity in cells caused by the combined injury. Results of flow cytometry and immunohistochemistry showed that pre-addition of guattegaumerine interrupted the apoptosis of the neurons, reversed the up regulation of the pro-apoptotic gene (Bax) and the down regulation of the anti-apoptotic gene (Bcl-2). Furthermore, guattegaumerine suppressed the increase of intracellular calcium ([Ca(2+)](i)) stimulated by either H(2)O(2) or KCl in Ca(2+)-containing extracellular solutions, and high concentration of 2.5 microM guattegaumerine also suppressed the increase of [Ca(2+)](i) induced by H(2)O(2) in Ca(2+)-free solution. These observations suggested that guattegaumerine may possess potential protection against oxidative stress injury, which might be beneficial for neurons.

Oxidative stress in primary glomerular diseases: a comparative study

OBJECTIVE

To evaluate the status of oxidative stress in patients with different primary glomerular diseases (PGD) which have differential predisposition to renal failure.

METHODS

Seventy-three patients with PGD and 50 controls were enrolled in the study. They were sub-grouped into non-proliferative glomerulonephritis (NPGN) and proliferative glomerulonephritis (PGN). Levels of serum malondialdehyde (MDA), reactive nitrogen intermediates (RNI), plasma total homocysteine (tHcy), urine 8-isoprostane (8-IP), RBC thiols, glutathione-S-transferase (GST) and serum superoxide dismutase (SOD) were measured spectrophotometrically.

RESULTS

PGD patients showed a significant increase in MDA, RNI, tHcy, 8-IP levels (P < 0.05) and decreased SOD, total thiols and protein bound thiol levels as compared to controls (P < 0.05). Significantly higher levels of tHcy, MDA and 8-IP (P < 0.05) and lower SOD enzyme activity (P < 0.05) were observed in PGN group as compared to NPGN and control groups. These changes remained significant even after adjustment was made for creatinine.

CONCLUSIONS

Oxidative stress in PGN is significantly higher than NPGN, indicating higher oxidative stress in these patients, independent of degree of renal dysfunction.

Decoding of calcium oscillations by phosphorylation cycles: analytic results

Experimental studies have demonstrated that Ca(2+)-regulated proteins are sensitive to the frequency of Ca(2+) oscillations, and several mathematical models for specific proteins have provided insight into the mechanisms involved. Because of the large number of Ca(2+)-regulated proteins in signal transduction, metabolism and gene expression, it is desirable to establish in general terms which molecular properties shape the response to oscillatory Ca(2+) signals. Here we address this question by analyzing in detail a model of a prototypical Ca(2+)-decoding module, consisting of a target protein whose activity is controlled by a Ca(2+)-activated kinase and the counteracting phosphatase. We show that this module can decode the frequency of Ca(2+) oscillations, at constant average Ca(2+) signal, provided that the Ca(2+) spikes are narrow and the oscillation frequency is sufficiently low--of the order of the phosphatase rate constant or below. Moreover, Ca(2+) oscillations activate the target more efficiently than a constant signal when Ca(2+) is bound cooperatively and with low affinity. Thus, the rate constants and the Ca(2+) affinities of the target-modifying enzymes can be tuned in such a way that the module responds optimally to Ca(2+) spikes of a certain amplitude and frequency. Frequency sensitivity is further enhanced when the limited duration of the external stimulus driving Ca(2+) signaling is accounted for. Thus, our study identifies molecular parameters that may be involved in establishing the specificity of cellular responses downstream of Ca(2+) oscillations.

Subcellular organization of calcium signalling in hepatocytes and the intact liver

Hepatocytes respond to inositol 1,4,5-trisphosphate (InsP3)-linked agonists with frequency-modulated oscillations in the intracellular free calcium concentration ([Ca2+]i), that occur as waves propagating from a specific origin within each cell. The subcellular distribution and functional organization of InsP3-sensitive Ca2+ pools has been investigated, in both intact and permeabilized cells, by fluorescence imaging of dyes which can be used to monitor luminal Ca2+ content and InsP3-activated ion permeability in a spatially resolved manner. The Ca2+ stores behave as a luminally continuous system distributed throughout the cytoplasm. The structure of the stores, an important determinant of their function, is controlled by the cytoskeleton and can be modulated in a guanine nucleotide-dependent manner. The nuclear matrix is devoid of Ca2+ stores, but Ca2+ waves in the intact cell propagate through this compartment. The organization of [Ca2+]i signals has also been investigated in the perfused liver. Frequency-modulated [Ca2+]i oscillations are still observed at the single cell level, with similar properties to those in the isolated hepatocyte. The [Ca2+]i oscillations propagate between cells in the intact liver, leading to the synchronization of [Ca2+]i signals across part or all of each hepatic lobule.

A mesoscopic stochastic mechanism of cytosolic calcium oscillations

Based on a model of intracellular calcium (Ca(2+)) oscillation with self-modulation of inositol 1,4,5-trisphosphate signal, the mesoscopic stochastic differential equations for the intracellular Ca(2+) oscillations are theoretically derived by using the chemical Langevin equation method. The effects of the finite biochemical reaction molecule number on both simple and complex cytosolic Ca(2+) oscillations are numerically studied. In the case of simple intracellular Ca(2+) oscillation, it is found that, with the increase of molecule number, the coherence resonance or autonomous resonance phenomena can occur for some external stimulation parameter values. In the cases of complex cytosolic Ca(2+) oscillations, each extremum of concentration of cytosolic Ca(2+) oscillations corresponds to a peak in the histogram of Ca(2+) concentration, and the most probability appeared during the bursting plateau level for bursting, but at the largest minimum of Ca(2+) concentration for chaos. For quasi-periodicity, however, there are only two peaks in the histogram of Ca(2+) concentration, and the most probability is located at low concentration state.

Purinergic signalling and intercellular Ca2+ wave propagation in the organ of Corti

Extracellular ATP is a key neuromodulator of visual and auditory sensory epithelia. In the rat cochlea, pharmacological dissection indicates that ATP, acting through a highly sensitive purinergic/IP(3)-mediated signaling pathway with (little or) no involvement of ryanodine receptors, is the principal paracrine mediator implicated in the propagation of calcium waves through supporting and epithelial cells. Measurement of sensitivity to UTP and other purinergic agonists implicate P2Y(2) and P2Y(4) as the main P2Y receptor isoforms involved in these responses. Ca2+ waves, elicited under highly reproducible conditions by carefully controlling dose (1 microM) and timing of focal agonist application (0.2s), extended over radial distance greater than 160 microm from the source, identical to those activated by damaging single outer hair cells. Altogether, these results indicate that intercellular calcium waves are a robust phenomenon that confers a significant ability for cell-cell communication in the mammalian cochlea. Further ongoing research will reveal the roles that such Ca2+ waves play in the inner ear.

Under what conditions signal transduction pathways are highly flexible in response to external forcing? A case study on calcium oscillations

Sensitivity and flexibility are typical properties of biological systems. These properties are here investigated in a model for simple and complex intracellular calcium oscillations. In particular, the influence of external periodic forcing is studied. The main point of the study is to compare responses of the system in a chaotic regime with those obtained in a regular periodic regime. We show that the response to external signals in terms of the range of synchronization is not significantly different in regular and chaotic Ca2+ oscillations. However, both types of oscillation are highly flexible in regimes with weak dissipation. Therefore, we conclude that dissipation of free energy is a suitable index characterizing flexibility. For biological systems this appears to be of special importance since for thermodynamic reasons, notably in view of low free energy consumption, dissipation should be minimized.

Intercellular communication via intracellular calcium oscillations

In this letter, we present the results of a simple model for intercellular communication via calcium oscillations, motivated in part by a recent experimental study. The model describes two cells (a "donor" and "sensor") whose intracellular dynamics involve a calcium-induced, calcium release process. The cells are coupled by assuming that the input of the sensor cell is proportional to the output of the donor cell. As one varies the frequency of calcium oscillations of the donor cell, the sensor cell passes through a sequence of N : M phase-locked regimes and exhibits a "Devil's staircase" behavior. Such a phase-locked response has been seen experimentally in pulsatile stimulation of single cells. We also study a stochastic version of the coupled two-cell model. We find that phase locking holds for realistic choices for the cell volume.

Modelling of simple and complex calcium oscillations. From single-cell responses to intercellular signalling

This review provides a comparative overview of recent developments in the modelling of cellular calcium oscillations. A large variety of mathematical models have been developed for this wide-spread phenomenon in intra- and intercellular signalling. From these, a general model is extracted that involves six types of concentration variables: inositol 1,4,5-trisphosphate (IP3), cytoplasmic, endoplasmic reticulum and mitochondrial calcium, the occupied binding sites of calcium buffers, and the fraction of active IP3 receptor calcium release channels. Using this framework, the models of calcium oscillations can be classified into 'minimal' models containing two variables and 'extended' models of three and more variables. Three types of minimal models are identified that are all based on calcium-induced calcium release (CICR), but differ with respect to the mechanisms limiting CICR. Extended models include IP3--calcium cross-coupling, calcium sequestration by mitochondria, the detailed gating kinetics of the IP3 receptor, and the dynamics of G-protein activation. In addition to generating regular oscillations, such models can describe bursting and chaotic calcium dynamics. The earlier hypothesis that information in calcium oscillations is encoded mainly by their frequency is nowadays modified in that some effect is attributed to amplitude encoding or temporal encoding. This point is discussed with reference to the analysis of the local and global bifurcations by which calcium oscillations can arise. Moreover, the question of how calcium binding proteins can sense and transform oscillatory signals is addressed. Recently, potential mechanisms leading to the coordination of oscillations in coupled cells have been investigated by mathematical modelling. For this, the general modelling framework is extended to include cytoplasmic and gap-junctional diffusion of IP3 and calcium, and specific models are compared. Various suggestions concerning the physiological significance of oscillatory behaviour in intra- and intercellular signalling are discussed. The article is concluded with a discussion of obstacles and prospects.

Noise enhanced hormonal signal transduction through intracellular calcium oscillations

In a wide range of non-linear dynamical systems, noise may enhance the detection of weak deterministic input signals. Here, we demonstrate this phenomenon for transmembrane signaling in a hormonal model system of intracellular Ca(2+) oscillations. Adding Gaussian noise to a subthreshold extracellular pulsatile stimulus increased the sensitivity in the dose-response relation of the Ca(2+) oscillations compared to the same noise signal added as a constant mean level. These findings may have important physiological consequences for the operation of hormonal and other physiological signal transduction systems close to the threshold level.

Coding efficiency and information rates in transmembrane signaling

A variety of cell types responds to hormonal stimuli by repetitive spikes in the intracellular concentration of calcium ([Ca(2+)](i)) which have been demonstrated to encode information in their frequency, amplitude, and duration. These [Ca(2+)](i)-spike trains are able to specifically regulate distinct cellular functions. Using a mathematical model for receptor-controlled [Ca(2+)](i) oscillations in hepatocytes we investigate the encoding of fluctuating hormonal signals in [Ca(2+)](i)-spike trains. The transmembrane information transfer is quantified by using an information-theoretic reverse-engineering approach which allows to reconstruct the dynamic hormonal stimulus from the [Ca(2+)](i)-spike trains. This approach allows to estimate the accuracy of coding as well as the rate of transmembrane information transfer. We found that up to 87% of the dynamic stimulus information can be encoded in the [Ca(2+)](i)-spike train at a maximum information transfer rate of 1.1 bit per [Ca(2+)](i)-spike. These numerical results for humoral information transfer are in the same order as in a number of sensory neuronal systems despite several orders of magnitude different time scales of operation suggesting a universal principle of information processing in both biological systems.

Vascular non-protein thiols: prooxidants or antioxidants in atherogenesis?

Abstract-cell-mediated lipoprotein oxidation may be due to generation of non-protein thiols (NP-SH) from cystine with formation of oxidizing species. However, NP-SH, especially GSH, may also exert antioxidant effects in vitro and in vivo. To further investigate whether vascular NP-SH could be prooxidants or antioxidants in atherosclerosis, we have correlated the aortic content of NP-SH with that of lipoperoxides in 10 rabbits fed on a fat-enriched atherogenic diet for 9 weeks. As compared to 7 control rabbits, aortic NP-SH and lipoperoxides were significantly increased in the fat-fed animals. The levels of NP-SH were strongly and inversely correlated with those of lipid peroxidation in the atherosclerotic aorta (r(s) -0.92, P < 0.0001 for thiobarbituric acid reactive substances, and r(s) -0.80, P < 0.01 for fluorescent damage products of lipid peroxidation). A similar trend was evident also in the control rabbits (r(s) -0.60 for both indices of lipid peroxidation). Thus, the present data suggest that vascular NP-SH exert significant antioxidant-antilipoperoxidative effects in vivo especially in fat diet-related atherogenic conditions.

Magnetic field perturbations as a tool for controlling enzyme-regulated and oscillatory biochemical reactions

The feasibility of magnetic field perturbations as a tool for controlling enzyme-regulated and oscillatory biochemical reactions is studied. Our approach is based on recent experimental results that revealed magnetic field effects on the in vitro activity of enzyme systems in accordance with the radical pair mechanism. A minimum model consisting of two coupled enzyme-regulated reactions is discussed that combines, in a self-consistent manner, magnetic field-sensitive enzyme kinetics with non-linear dynamical principles. Furthermore, a simple detector mechanism is described that is capable of responding to an oscillatory input. Results reveal that moderate-strength magnetic fields (B=1-100 mT) may effectively alter the dynamics of the system. In particular, a response behavior is observed that depends on: (1) the combination of static and time-varying magnetic fields; (2) the field amplitude; and (3) the field frequency in a non-linear fashion. The specific response behavior is critically determined by the biochemical boundary conditions as defined by the kinetic properties of the system. We propose an experimental implementation of the results based on the oscillatory peroxidase-oxidase reaction controlled by the enzyme horseradish peroxidase.

Effects on the hepatocyte [Ca2+]i oscillator of inhibition of the plasma membrane Ca2+ pump by carboxyeosin or glucagon-(19-29)

Single rat hepatocytes, microinjected with the Ca(2+)-sensitive photoprotein aequorin, respond to agonists acting through the phosphoinositide signalling pathway by the generation of oscillations in cytosolic free Ca2+ concentration ([Ca2+]i). The duration of [Ca2+]i transients generated is characteristic of the receptor species activated; the variability results in differences in the rate of fall of [Ca2+]i from its peak. It is conceivable that the plasma membrane Ca(2+)-ATPase (PM Ca2+ pump) may have an important role in the mechanism underlying agonist specificity. It has recently been shown that an esterified form of carboxyeosin, an inhibitor of the red cell PM Ca2+ pump, is suitable for use in whole cell studies. Glucagon-(19-29) (mini-glucagon) inhibits the Ca2+ pump in liver plasma membranes, mediated by Gs. We show here that carboxyeosin and mini-glucagon inhibit Ca2+ efflux from populations of intact rat hepatocytes. We show that carboxyeosin and mini-glucagon enhance the frequency of oscillations induced by Ca(2+)-mobilizing agonists in single hepatocytes, but do not affect the duration of individual transients. Furthermore, we demonstrate that inhibition of the hepatocyte PM Ca2+ pump enables the continued generation of [Ca2+]i oscillations for a prolonged period following the removal of extracellular Ca2+.

Self-organized segmentation of time series: separating growth hormone secretion in acromegaly from normal controls

The pulsatile pattern of growth hormone (GH) secretion was assessed by sampling blood every 10 min over 24 h in healthy subjects (n = 10) under normal food intake and under fasting conditions (n = 6) and in patients with a GH-producing tumor (acromegaly, n = 6), before and after treatment with the somatostatin analog octreotide. Using autocorrelation, we found no consistent separation in the temporal dynamics of GH secretion in healthy controls and acromegalic patients. Time series prediction based on a single neural network has recently been demonstrated to separate the secretory dynamics of parathyroid hormone in healthy controls from osteoporotic patients. To better distinguish the differences in GH dynamics in healthy subjects and patients, we tested time series predictions based on a single neural network and a more refined system of multiple neural networks acting in parallel (adaptive mixtures of local experts). Both approaches significantly separated GH dynamics under the various conditions. By performing a self-organized segmentation of the alternating phases of secretory bursts and quiescence of GH, we significantly improved the performance of the multiple network system over that of the single network. It thus may represent a potential tool for characterizing alterations of the dynamic regulation associated with diseased states.

Frequency encoding in excitable systems with applications to calcium oscillations

A number of excitable cell types respond to a constant hormonal stimulus with a periodic oscillation in intracellular calcium. The frequency of oscillation is often proportional to the hormonal stimulus, and one says that the stimulus is frequency encoded. Here we develop a theory of frequency encoding in excitable systems and apply it to intracellular calcium oscillations that results from increases in the intracellular level of inositol 1,4,5-triphosphate.

Transmural distribution of antioxidant defences and lipid peroxidation in the rabbit left ventricular myocardium

The left ventricular subendocardial and subepicardial layers of six perfused rabbit hearts were tested for enzymatic and non-enzymatic antioxidant defences and for lipid peroxidation. The subendocardium showed significantly lower catalase activity and contents of non-protein thiol compounds and vitamin E associated with a higher degree of lipid peroxidation. The activities of Cu,Zn- and Mn-superoxide dismutases, glutathione reductase, gamma-glutamylcysteine synthetase and gamma-glutamyl transpeptidase showed no significant transmural differences, and Se-independent glutathione peroxidase activity was not detectable in either layer. Comparable results were observed in another group of six unperfused rabbit hearts. In five H2O2-perfused rabbit hearts, lipid peroxidation was higher, and myocardial creatine phosphokinase activity lower, in the subendocardium than in the subepicardium. In this group, only the subendocardium had significantly higher lipid peroxidation levels than the control hearts. Thus, a lower antioxidant capacity and a greater oxidative stress are present in the rabbit subendocardium. These findings could provide insight into the problem of subendocardial vulnerability to free radical-mediated processes, such as occurs in ischaemia-reperfusion injury.

Mechanisms of cellular information processing

Living cells in multicellular organisms are in simultaneous contact with many regulatory factors such as hormones or neurotransmitters. Many of these factors vary with time in their local concentrations, owing to pulsatile release or production. Therefore, complex patterns of signaling factors act on each living cell in vivo, stimulating or inhibiting second-messenger pathways with potentially complex dynamics. These intracellular pathways do not operate independently but are extensively interconnected, creating complex networks and patterns of intracellular signals that combine to determine the cell's response. The potential significance of cross-signaling between second-messenger pathways and of dynamic stimulation of receptors for cellular information processing in physiology and pathophysiology are discussed.